Gauge symmetries are one of the concepts that can be studied in constrained systems. In order to investigate this symmetries we can use Hamiltonian and Lagrangian approaches separately. Through this thesis we choose to work with the latter. In this approach we deduce Noether identities by using equations of motion. Also these identities contain generators of gauge transformations. By the use of these generators, gauge transformations could be written for dynamical variables. Furthermore by introducing the systematic non-covariant approach and deriving the gauge transformation generators, symmetries of generalized Schwinger models are studied. After that using the above approach another non-covariant approach which is called ''testing method" has been studied. With this last method, the symmetries of Yang-Mills, electromagnetism, general relativity and topologically massive gravity theories are studied. Finally, the above testing method is presented in a covariant form and by investigating symmetries of above theories in the covariant form, advantages of using this approach compared with non-covariant is illustrated.